Switching between them in single player a la Banjo Tooie could've made for some cool gameplay, but at least it's drop-in/drop-out besides the intro; being stuck with an AI companion cos you started your file in single player would've been a pain.
The hissy fits about Bayonetta 2 being Wii U exclusive is a sad testament to how entitled, rude, and childish gamers today can be. It makes all gamers look bad.
When you first start, up until you get to Mean Street, you're in single player mode, after you're at Mean Street however, it's drop-in/drop-out two player mode for the rest of the game (The second player uses the 2 button on their controller to take over Oswald). This gives you the flexibility of having a friend show up mid-game and joining you and then giving the AI control again if they wanna step away.
Also: Only the Wii-Mote+Nunchuk control scheme in the Wii version.